Direct Discretization Method for Realizing a Class of Fractional Order System in Delta Domain – a Unified Approach

Abstract

Discretization is fundamental for digital realization of the fractional order system. The fractional order systems are digitally implemented by using either indirect or direct discretization methods. All these methods are typically developed in the conventional z domain in the form of s to z transforms. In this paper, a new direct discretization method is presented as a substitute of conventional z domain direct discretization method. The proposed approach capitalizes the feature of delta operator to unify both the discretized system and its continuous-time counterpart at the lower sampling time limit. The discretization is accomplished in two stages. At first, the delta operator is reframed by using the trapezoidal quadrature rule to obtain the suitable generating function. Then, the generating function is further expanded using the continued fraction expansion method to obtain the discrete-time approximation of the fractional order differentiator. Illustrative examples are presented to exhibit the efficacy of the proposed method with respect to two prevalent direct discretization methods of z domain on the basis of simulation results obtained using MATLAB.